1 Introduction

High-level radioactive waste (HLW) arising from the spent fuel of nuclear power plants is increasing with the development of nuclear energy. Given the nature of HLW, in particular that it contains high concentrations of long-lived fission products (LLFPs), Pu and minor actinides (MAs), its disposal has become an urgent problem facing the nuclear industry ^[1]. At present, one of the most promising methods for dealing with HLW is partition and transmutation (P&T) ^[2]. The accelerator-driven sub-critical system (ADS) is a facility that can be used as a neutron source for transmuting MAs. The ADS is a hybrid system that comprises a high intensity proton accelerator, a spallation target and a sub-critical reactor. Protons are injected into the spallation target to produce neutrons that then drive the sub-critical reactor core. The target is made of heavy metals (HMs) in solid or liquid state. Compared to a traditional critical reactor, the sub-critical reactor of an ADS has a higher-energy neutron energy spectrum, higher flux and wider energy distribution, which can be used to transmute MAs and LLFPs ^[3]. The reactivity margin of an ADS to prompt criticality can be increased by an extra margin that does not depend on delayed neutrons. This enables the safe operation of a core with degraded characteristics, for example, if pure MA burners are used, excess reactivity can be eliminated, allowing the design of cores with a reduced potential for reactivity-induced accidents ^[4]. The ADS has been studied in many nations, for example, the initial Accelerator-Driven System (CiADS) program in China ^[5]; the multipurpose accelerator-driven system for research & development (MYRRHA) in Belgium ^[6]; the OMEGA program and the high intensity proton accelerator project in Japan (J-PARC) ^[7,8]; and the research program on separation–incineration (SPIN) in France ^[9].

In this study, the initial design parameters were as follows: 1) Pu and MA content of fuel; 2) the inert matrix materials; 3) type of coolant; 4) type of cladding and its thickness; 5) height, material and structure of shielding; 6) reflector height and components; 7) core activity zone height; 8) type of fuel pellet; 9) fuel component structure; and 10) proton beam energy. The search parameters were initial Pu loading, the type of inert matrix and the number of fuel assemblies.

Change in the effective multiplication factor (k_eff) are important in the design of an ADS core ^[10]. The purpose of this study was to establish those core design parameters that will give rise to little k_eff variation within 500 d of full power operation. Another significant aspect of ADS design is achieving a low transmutation supplier-to-burner support ratio^[11]. In order to improve the characteristics of MA transmutation, the impacts of initial loading of MAs on the efficiency of MA transmutation were investigated. In Sect. 2, the method of burnup calculation and fuel design are introduced. In Sect.3, fuel burn up characteristic parameters are determined and analyzed. In Sect. 4, the results of calculations and analyses for long-period refueling fuel burnup of an ADS are presented.

2 Computational methods and software

2.2 Fuel for MA transmutation

For the core fuel, a mixture of mono-nitrides of MAs and Pu was used ^[17]. Zirconium-nitride (ZrN) was also used in the fuel elements as an inert matrix. Nitrogen with N-15 enriched (100%) was used for (Pu, MA)-nitride and ZrN. Nitrides have suitable physical properties, and Pu and MAs do not have resonance cross sections in the fast neutron energy range (Fig. 1) ^[18]. Nitrides can also be made into a cylindrical shape, which reduces the space self-shielding effect. Moreover, in the fast neutron region, the capture cross sections of MAs decrease with increased neutron energy, whereas the fission cross section increases with increased neutron energy and the capture-to-fission ratios increase. Lead–bismuth was used as the coolant to reduce the moderating effect of neutrons and this ensured that a hard neutron energy spectrum was maintained in the active core region that would be more conducive to the transmutation of MAs.

Figure 1Full-screen View

(Color online) Capture and fission cross section of a selection of MAs.

The production and isotopic composition of MAs and Pu from their originating the Pressurized Water Reactror (PWR) are shown in Tables 1 and 2; the power of the PWR was 1 GWe, equivalent to 3.3 GWth. The operation time was one year, the fuel burnup depth was 33 GWd/t and the cooling time was 3 years ^[19]. The Specific Ability for MA Production (SAMAP) was 23.81/3.3≈7.2 kg Gwt⁻¹ a⁻¹.

Table 1Full-screen View

Isotopic composition ratio of MAs ^[19]

Nuclide	T1/2 (a)	m (kg Gwe−1 a−1)	Mass composition (wt. %)
237Np	2.144×106	13.38	56.2
241Am	432.6	6.28	26.4
243Am	7364	2.86	12.0
243Cm	29.1	7.14×10-3	0.03
244Cm	18.1	1.22	5.11
245Cm	8423	6.67×10-2	0.28
Total		23.81

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Table 2Full-screen View

Isotopic composition ratio of Pu ^[20]

Isotope	T1/2 (a)	Mass composition (wt.%)
238Pu	87.7	1.81
239Pu	2.411×104	59.14
240Pu	6561	22.96
241P	14.329	12.13
242Pu	3.75×105	3.96

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3 Search for core design scheme

The search for the ADS was conducted using the total loading mass of Pu, the number of fuel assemblies and the total amount of inert matrix. However, there were some fixed parameters in the ADS and they are listed in Table 3. The calculation flow for the parametric search is shown in Fig.2.

Figure 2Full-screen View

Calculation flow for the parametric survey calculations.

The core thermal power was 800 MW and burnup history was 500 EFPDs. In this study, the MA inventory was fixed at 3000 kg of initial core. For all cases, the initial core k_eff was set to 0.97, whereas the parametric survey and fuel burnup analysis were carried out by adjusting the number of fuel assemblies, the amount of Pu of the initial loading and the total amount of inert matrix. The main purpose of the parameter search was to define the ADS core whose k_eff decreased over the 500 EFPDs and was between 0.9590 and 0.9705. After the fuel loading scheme was determined, the core burnup was calculated over the longer period of 3600 EFPDs.

Following a series of calculations, five cases of different Pu loadings were derived and the parameters of each scheme are shown in Table 4.

From the results of the search for a core design scheme, the following conclusions applicable to all five cases were drawn:

1.With the initial loading amount of MAs and Pu and the loading amount of inert matrix fixed, the more fuel assemblies in the core and the larger the core volume, the smaller the fuel density and the smaller the core k_eff in the initial state.

2.With the initial loading of MAs and Pu fixed, the percentage of inert matrix increased and the fuel density increased, while the core structure of the ADS remained unchanged. The larger the percentage of inert matrix, the smaller the k_eff.

3.With the number of fuel components and MA initial loading fixed, the heavy metals (HMs) increased with the increase of Pu initial loading. In order to make the initial k_eff of the ADS reach 0.97, the inert matrix must be increased.

The burnup calculation of every case was performed by code COUPLE3.0. The change of k_eff over 500 EFPDs was obtained and is shown in Fig. 3.

Figure 3Full-screen View

Time evolution of the effective multiplication factor (k_eff) for different cases.

Figure 3 shows that the k_eff of cases 1 to 4 decreased with the increase of burnup time, and the higher the initial loading of Pu (MA 3000 kg), the greater the change of k_eff over the consumption time. In contrast, the k_eff of the case defined as CASE 5 increased during the burnup history. The reason for this trend is that the percentage of MA loading was too high, the k_eff increased with the increase of fuel consumption time, and the k_eff increased up to the end of the 500 d cycle. Hence the percentage of MA to HM should be limited to an appropriate value. The ADS system met the calculation requirements when the initial Pu was 30.6% of the initial mass composition in the heavy metal component (IHM) and the loading of the inert matrix was 63.69% IHM. The final solution was therefore found to be CASE 4.

4 Burnup analysis of sub-critical core

CASE 4 represented the sub-critical reactor core shown in Fig.4. It consisted mainly of four zones including the target fuel, reflector and shielding assemblies and lead-bismuth eutectic (LBE).

Figure 4Full-screen View

(Color online) Radial profile of the ADS core.

The initial k_eff of the ADS core was 0.97009 and the reactivity was -3083 pcm. The entire core consisted of 78 fuel assemblies, 36 reflector assemblies and 90 shielding layer assemblies. Each fuel assembly contained 265 fuel elements and 6 lead-bismuth channels. In the calculation of long burnup period, 600 EFPDs was a burnup cycle and the total burnup time was 3600 EFPDs. In code COUPLE3.0, the fuel assembly were numbered as shown in Figure 5.

Figure 5Full-screen View

Fuel assembly labeling scheme.

Table 5 shows the material numbers (1001–1045) of each of the fuel assemblies used in different burnup cycles. In the initial state, each labeled fuel assembly had a corresponding fuel material number. After operation over the first 600 EFPDs, fuel material numbers 1001 to 1006 inclusive in the inner ring fuel assemblies were moved outside the core; 1007 to 1013 inclusive, which had been irradiated for 600 EFPDs in the outer ring fuel assemblies, were relocated to the inner ring regions; and new fuel material numbers 1014 to 1019 inclusive were moved to the outer ring region. The burnup analysis was carried out in this way for 6 fuel cycles.

The changes in total mass of Pu and mass ratio of Pu to heavy metal (HM) over 3600 EFPDs are shown in Fig. 6(a), and changes of total mass of MAs and mass ratio of MAs to IHM over 3600 EFPDs are shown in Fig. 6(b). In each fuel cycle, with the increase of burnup time, the total mass of MAs decreased, the total mass of Pu increased, and the mass percentage of Pu in HM increased continuously. The main reason for this is that ²³⁷Np (in the MAs) generated ²³⁸Pu, and the increase of all isotopes of Pu was greater than the loss. Refueling every 600 d was according to the fuel material provided in Table 5.

Figure 6Full-screen View

Change of total mass and mass ratio of Pu (a) and MAs (b) in heavy metal.

Variation of the core amplification factor over time is shown in Fig. 7. The core amplification factor is the weight of loss to fission per proton multiplied by E_fission/E_beam. In each fuel cycle, with increased burnup time, the core amplification factor continuously decreased. After replacement with new fuel, the core amplification factor increased significantly. The main reason for this was that in each fuel cycle, with the increase of time, part of the core fuel was consumed and the fuel available for fission reactions in the core decreased, which led to a decrease in the amplification factor. The maximum difference in the value of the core amplification factor during the whole cycle was 44.17%.

Figure 7Full-screen View

Variation of core amplification factor over time.

Variation of k_eff over time is shown in Fig. 8. k_eff decreased within each fuel cycle, but then increased when new fuel was introduced to the reactor. The main reason for the decreases in k_eff was that in each fuel cycle, increasing fuel consumption of the core resulted in a decrease in the number of newly generated neutrons in the core, which led to a decrease in the core k_eff. Variation of the maximum power density over time is shown in Fig. 9, and ranges from 256.00 to 274.14 W/cm³, which is a relatively small change.

Figure 8Full-screen View

Variation of effective multiplication factor over time.

Figure 9Full-screen View

Variation of core maximum power density over time.

Neutron energy spectrum in the initial ADS is shown in Fig. 10. The figure shows the ADS had a hard neutron energy spectrum and the energy range of the neutron energy spectrum was wide. Changes in the mass percent of the major isotopes of Pu over time are shown in Figure 11. Over each fuel cycle, the mass compositions of ²³⁹Pu, ²⁴⁰Pu and ²⁴¹Pu decreased, while those of ²³⁸Pu and ²⁴²Pu increased. After refueling, the mass compositions of ²³⁹Pu, ²⁴⁰Pu and ²⁴¹Pu increased, while those of ²³⁸Pu and ²⁴²Pu decreased. The main reason behind these observations is that in each fuel cycle, the total mass of Pu increased constantly, but the mass compositions of ²³⁹Pu and ²⁴¹Pu decreased because the decrease in their masses was greater than their rate of generation. The total mass of ²⁴⁰Pu in the core increased, but ²⁴⁰Pu mass ratio decreased as the total Pu mass increased. Furthermore, a large amount of ²³⁸Pu was transmuted from ²³⁸Np through β decay, ²³⁹Pu through (n,2n) reaction and ²⁴²Cm through α decay. The disappearance rate of ²³⁸Pu was far less than its rate of generation, which led to a relatively large increase of ²³⁸Pu mass in the core, and a continuous increase of ²³⁸Pu mass percent. The rate of disappearance of ²⁴²Pu was less than its generation rate, and therefore the core ²⁴²Pu mass increased, and ²⁴²Pu mass composition increased continuously. After refueling, Pu total mass decreased, and ²³⁹Pu and ²⁴¹Pu mass increased, resulting in increased ²³⁹Pu and ²⁴¹Pu mass ratios. The mass of ²⁴⁰Pu decreased, but the reduction was not as great as the reduction of Pu total mass, so the mass ratio of ²⁴⁰Pu increased. The mass of ²³⁸Pu increased, Pu total mass decreased, and therefore the mass composition of ²³⁸Pu decreased. The mass of ²⁴²Pu decreased, but its mass reduction was less than the mass of total Pu, resulting in the decrease in the mass composition of ²⁴²Pu.

Figure 10Full-screen View

Neutron energy spectrum in the initial ADS.

Figure 11Full-screen View

Changes in the mass ratio of the major isotopes of Pu.

Changes in the mass percent of the major isotopes of MAs over time are shown in Figure 12. Over each fuel cycle, the mass compositions of ²³⁷Np and ²⁴¹Am decreased, while those of ²⁴²Cm and ²⁴⁴Cm increased and those of ^241mAm, ²⁴³Am, ²⁴³Cm and ²⁴⁵Cm remained stable. After refueling, the mass compositions of ²³⁷Np and ²⁴¹Am increased, while those of ²⁴²Cm and ²⁴⁴Cm decreased and those of ^241mAm, ²⁴³Am, ²⁴³Cm and ²⁴⁵Cm remained stable. The main reason behind these observations is that in each fuel cycle, the total mass of the MAs decreased, and the decrease of ²³⁷Np and ²⁴¹Am in their masses was greater than their rate of generation, and the reduction in their masses was greater than the decrease of the total mass of MA, and therefore the mass compositions of ²³⁷Np and ²⁴¹Am decreased. The total masses of ²⁴²Cm and ²⁴⁴Cm increased and their mass compositions increased; the mass changes of ^241mAm, ²⁴³Am, ²⁴³Cm and ²⁴⁵Cm were similar to that of the total mass of MAs, so their mass compositions did not change much in the entire burnup cycle. After refueling, MAs total mass increased, and ²³⁷Np and ²⁴¹Am masses increased, which were larger than the increase of the total mass of MAs, resulting in increased ²³⁷Np and ²⁴¹Am mass ratios. The masses of ²⁴²Cm and ²⁴⁴Cm decreased and MAs total mass increased, resulting in a decreased mass ratio of ²⁴²Cm and ²⁴⁴Cm in MAs.

Figure 12Full-screen View

Changes in the mass ratio of the major isotopes of MAs.

Variation of the above defined terms versus burnup time is shown in Fig.13. Through 3600 EFPDs of the operation, the ΔM_MA was -3555.2 kg, ΔM_MA→Pu→U was 21.3 kg, ΔM_MA→Pu was 1938.9 kg, and ΔM_MA→TRMA was 5.8E-4 kg, which meant that ΔM_MA(EFF) was -1594.9 kg. Therefore, for the designed sub-critical reactor, the Specific Ability for MA Transmutation (SAMAT) was 1594.9/(0.8×3600/365)=202.1 kg Gwt⁻¹ a⁻¹.

Figure 13Full-screen View

ΔM_MA, ΔM_MA→Pu→U, ΔM_MA→Pu, ΔM_MA→TRMA, ΔM_MA(EFF) with depletion time.

The efficient transmutation Supplier-to-Burner Support Ratio (SBSR) is SAMAT/SAMAP. Therefore for this ADS, the SBSR was 202.1/7.2≈28, demonstrating that this ADS was efficient at MA transmutation.

5 Conclusion

The physical study of a sub-critical reactor of an ADS with a thermal power of 800 MW for the purposes of MA transmutation was undertaken. The initial loading of MAs was 3000 kg and the fuel type was a mixture of mono-nitrides of MAs and Pu. Zirconium-nitride (ZrN) was used in the fuel as an inert matrix. The analysis of the burnup characteristics was performed using the code COUPLE3.0. In order to ensure small changes in k_eff and safety of the sub-critical core, refueling was undertaken every 600 d. Over each fuel cycle, the total mass of MAs decreased, the total mass of Pu increased, and the mass ratio of Pu increased constantly. After refueling, the total mass of MAs increased, the total mass of Pu decreased, and the corresponding mass composition of Pu decreased. In addition, the k_eff and core amplification factor decreased with burnup time, but both increased after refueling. The range of the maximum power density change was 256.00~274.14 W/cm³. The efficient transmutation Supplier-to-Burner Support Ratio (SBSR) of the selected sub-critical core design was about 28, demonstrating that this ADS was efficient at MA transmutation.